Dynamics and density function of a HTLV-1 model with latent infection and Ornstein-Uhlenbeck process

Yan Ren; Yan Cheng; Yuzhen Chai; Ping Guo; Yan Ren; Yan Cheng; Yuzhen Chai; Ping Guo

doi:10.3934/math.20241728

AIMS Mathematics

2024, Volume 9, Issue 12: 36444-36469. doi: 10.3934/math.20241728

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Research article

Dynamics and density function of a HTLV-1 model with latent infection and Ornstein-Uhlenbeck process

College of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China

Received: 17 September 2024 Revised: 25 November 2024 Accepted: 04 December 2024 Published: 31 December 2024
MSC : 60H10, 37A50

This paper examines the propagation dynamics of a T-lymphoblastic leukemia virus type Ⅰ (HTLV-1) infection model in a stochastic environment combined with an Ornstein-Uhlenbeck process. In conjunction with the theory of Lyapunov functions, we initially demonstrate the existence of a unique global solution to the model when initial values are positive. Subsequently, we establish a sufficient condition for the existence of a stochastic model stationary distribution. Based on this condition, the local probability density function expression of the model near the quasi-equilibrium point is solved by combining it with the Fokker-Planck equation. Subsequently, we delineate the pivotal conditions that precipitate the extinction of the disease. Finally, we select suitable data for numerical simulation intending to corroborate the theorem previously established.
- stochastic HTLV-1 infection model,
- Lyapunov function,
- ergodic stationary distribution,
- probability density function,
- extinction
Citation: Yan Ren, Yan Cheng, Yuzhen Chai, Ping Guo. Dynamics and density function of a HTLV-1 model with latent infection and Ornstein-Uhlenbeck process[J]. AIMS Mathematics, 2024, 9(12): 36444-36469. doi: 10.3934/math.20241728

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Abstract

This paper examines the propagation dynamics of a T-lymphoblastic leukemia virus type Ⅰ (HTLV-1) infection model in a stochastic environment combined with an Ornstein-Uhlenbeck process. In conjunction with the theory of Lyapunov functions, we initially demonstrate the existence of a unique global solution to the model when initial values are positive. Subsequently, we establish a sufficient condition for the existence of a stochastic model stationary distribution. Based on this condition, the local probability density function expression of the model near the quasi-equilibrium point is solved by combining it with the Fokker-Planck equation. Subsequently, we delineate the pivotal conditions that precipitate the extinction of the disease. Finally, we select suitable data for numerical simulation intending to corroborate the theorem previously established.

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